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<div class="titlepage"><div><div><h2 class="title" style="clear: both">
<a name="boost_random.tutorial"></a><a class="link" href="tutorial.html" title="Tutorial">Tutorial</a>
</h2></div></div></div>
<div class="toc"><dl class="toc">
<dt><span class="section"><a href="tutorial.html#boost_random.tutorial.generating_integers_in_a_range">Generating
      integers in a range</a></span></dt>
<dt><span class="section"><a href="tutorial.html#boost_random.tutorial.generating_integers_with_different_probabilities">Generating
      integers with different probabilities</a></span></dt>
<dt><span class="section"><a href="tutorial.html#boost_random.tutorial.generating_a_random_password">Generating
      a random password</a></span></dt>
<dt><span class="section"><a href="tutorial.html#boost_random.tutorial.generating_quasi_random_line_sphere_intersections">Generating
      quasi-random line-sphere intersections</a></span></dt>
</dl></div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.tutorial.generating_integers_in_a_range"></a><a class="link" href="tutorial.html#boost_random.tutorial.generating_integers_in_a_range" title="Generating integers in a range">Generating
      integers in a range</a>
</h3></div></div></div>
<p>
        For the source of this example see <a href="../../..//libs/random/example/die.cpp" target="_top">die.cpp</a>.
        First we include the headers we need for <code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code>
        and <code class="computeroutput"><a class="link" href="../boost/random/uniform_int_distribution.html" title="Class template uniform_int_distribution">uniform_int_distribution</a></code>.
      </p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">mersenne_twister</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">uniform_int_distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<p>
      </p>
<p>
        We use <code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code> with the
        default seed as a source of randomness. The numbers produced will be the
        same every time the program is run. One common method to change this is to
        seed with the current time (<code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">time</span><span class="special">(</span><span class="number">0</span><span class="special">)</span></code>
        defined in ctime).
      </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">mt19937</span> <span class="identifier">gen</span><span class="special">;</span>
</pre>
<p>
      </p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top"><p>
          We are using a <span class="emphasis"><em>global</em></span> generator object here. This
          is important because we don't want to create a new <a class="link" href="reference.html#boost_random.reference.concepts.pseudo_random_number_generator" title="Pseudo-Random Number Generator">pseudo-random
          number generator</a> at every call
        </p></td></tr>
</table></div>
<p>
        Now we can define a function that simulates an ordinary six-sided die.
      </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">roll_die</span><span class="special">()</span> <span class="special">{</span>
    <a class="co" name="boost_random.tutorial.generating_integers_in_a_range.c0" href="tutorial.html#boost_random.tutorial.generating_integers_in_a_range.c1"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">uniform_int_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">dist</span><span class="special">(</span><span class="number">1</span><span class="special">,</span> <span class="number">6</span><span class="special">);</span>
    <a class="co" name="boost_random.tutorial.generating_integers_in_a_range.c2" href="tutorial.html#boost_random.tutorial.generating_integers_in_a_range.c3"><img src="../../../doc/src/images/callouts/2.png" alt="2" border="0"></a><span class="keyword">return</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">gen</span><span class="special">);</span>
<span class="special">}</span>
</pre>
<p>
      </p>
<div class="calloutlist"><table border="0" summary="Callout list">
<tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_integers_in_a_range.c1"></a><a href="#boost_random.tutorial.generating_integers_in_a_range.c0"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> </p></td>
<td valign="top" align="left">
<p>
            <code class="computeroutput"><a class="link" href="../boost/random/mt19937.html" title="Type definition mt19937">mt19937</a></code> produces
            integers in the range [0, 2<sup>32</sup>-1]. However, we want numbers in the range
            [1, 6]. The distribution <code class="computeroutput"><a class="link" href="../boost/random/uniform_int_distribution.html" title="Class template uniform_int_distribution">uniform_int_distribution</a></code>
            performs this transformation.
          </p>
<div class="warning"><table border="0" summary="Warning">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Warning]" src="../../../doc/src/images/warning.png"></td>
<th align="left">Warning</th>
</tr>
<tr><td align="left" valign="top"><p>
              Contrary to common C++ usage <code class="computeroutput"><a class="link" href="../boost/random/uniform_int_distribution.html" title="Class template uniform_int_distribution">uniform_int_distribution</a></code>
              does not take a <span class="emphasis"><em>half-open range</em></span>. Instead it takes
              a <span class="emphasis"><em>closed range</em></span>. Given the parameters 1 and 6,
              <code class="computeroutput"><a class="link" href="../boost/random/uniform_int_distribution.html" title="Class template uniform_int_distribution">uniform_int_distribution</a></code>
              can produce any of the values 1, 2, 3, 4, 5, or 6.
            </p></td></tr>
</table></div>
</td>
</tr>
<tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_integers_in_a_range.c3"></a><a href="#boost_random.tutorial.generating_integers_in_a_range.c2"><img src="../../../doc/src/images/callouts/2.png" alt="2" border="0"></a> </p></td>
<td valign="top" align="left"><p>
            A distribution is a function object. We generate a random number by calling
            <code class="computeroutput"><span class="identifier">dist</span></code> with the generator.
          </p></td>
</tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.tutorial.generating_integers_with_different_probabilities"></a><a class="link" href="tutorial.html#boost_random.tutorial.generating_integers_with_different_probabilities" title="Generating integers with different probabilities">Generating
      integers with different probabilities</a>
</h3></div></div></div>
<p>
        For the source of this example see <a href="../../..//libs/random/example/weighted_die.cpp" target="_top">weighted_die.cpp</a>.
      </p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">mersenne_twister</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">discrete_distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

<span class="identifier">boost</span><span class="special">::</span><span class="identifier">mt19937</span> <span class="identifier">gen</span><span class="special">;</span>
</pre>
<p>
      </p>
<p>
        This time, instead of a fair die, the probability of rolling a 1 is 50% (!).
        The other five faces are all equally likely.
      </p>
<p>
        <code class="computeroutput"><a class="link" href="../boost/random/discrete_distribution.html" title="Class template discrete_distribution">discrete_distribution</a></code>
        works nicely here by allowing us to assign weights to each of the possible
        outcomes.
      </p>
<div class="tip"><table border="0" summary="Tip">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Tip]" src="../../../doc/src/images/tip.png"></td>
<th align="left">Tip</th>
</tr>
<tr><td align="left" valign="top"><p>
          If your compiler supports <code class="computeroutput"><span class="identifier">std</span><span class="special">::</span><span class="identifier">initializer_list</span></code>,
          you can initialize <code class="computeroutput"><a class="link" href="../boost/random/discrete_distribution.html" title="Class template discrete_distribution">discrete_distribution</a></code>
          directly with the weights.
        </p></td></tr>
</table></div>
<p>
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">probabilities</span><span class="special">[]</span> <span class="special">=</span> <span class="special">{</span>
    <span class="number">0.5</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.1</span><span class="special">,</span> <span class="number">0.1</span>
<span class="special">};</span>
<span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">discrete_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">probabilities</span><span class="special">);</span>
</pre>
<p>
      </p>
<p>
        Now define a function that simulates rolling this die.
      </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">int</span> <span class="identifier">roll_weighted_die</span><span class="special">()</span> <span class="special">{</span>
    <a class="co" name="boost_random.tutorial.generating_integers_with_different_probabilities.c0" href="tutorial.html#boost_random.tutorial.generating_integers_with_different_probabilities.c1"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a><span class="keyword">return</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">gen</span><span class="special">)</span> <span class="special">+</span> <span class="number">1</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
      </p>
<div class="calloutlist"><table border="0" summary="Callout list"><tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_integers_with_different_probabilities.c1"></a><a href="#boost_random.tutorial.generating_integers_with_different_probabilities.c0"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> </p></td>
<td valign="top" align="left"><p>
            Add 1 to make sure that the result is in the range [1,6] instead of [0,5].
          </p></td>
</tr></table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.tutorial.generating_a_random_password"></a><a class="link" href="tutorial.html#boost_random.tutorial.generating_a_random_password" title="Generating a random password">Generating
      a random password</a>
</h3></div></div></div>
<p>
        For the source of this example see <a href="../../..//libs/random/example/password.cpp" target="_top">password.cpp</a>.
      </p>
<p>
        This example demonstrates generating a random 8 character password.
      </p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">random_device</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">uniform_int_distribution</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">iostream</span><span class="special">&gt;</span>

<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span> <span class="special">{</span>
    <a class="co" name="boost_random.tutorial.generating_a_random_password.c0" href="tutorial.html#boost_random.tutorial.generating_a_random_password.c1"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a><span class="identifier">std</span><span class="special">::</span><span class="identifier">string</span> <span class="identifier">chars</span><span class="special">(</span>
        <span class="string">"abcdefghijklmnopqrstuvwxyz"</span>
        <span class="string">"ABCDEFGHIJKLMNOPQRSTUVWXYZ"</span>
        <span class="string">"1234567890"</span>
        <span class="string">"!@#$%^&amp;*()"</span>
        <span class="string">"`~-_=+[{]}\\|;:'\",&lt;.&gt;/? "</span><span class="special">);</span>
    <a class="co" name="boost_random.tutorial.generating_a_random_password.c2" href="tutorial.html#boost_random.tutorial.generating_a_random_password.c3"><img src="../../../doc/src/images/callouts/2.png" alt="2" border="0"></a><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">random_device</span> <span class="identifier">rng</span><span class="special">;</span>
    <a class="co" name="boost_random.tutorial.generating_a_random_password.c4" href="tutorial.html#boost_random.tutorial.generating_a_random_password.c5"><img src="../../../doc/src/images/callouts/3.png" alt="3" border="0"></a><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">uniform_int_distribution</span><span class="special">&lt;&gt;</span> <span class="identifier">index_dist</span><span class="special">(</span><span class="number">0</span><span class="special">,</span> <span class="identifier">chars</span><span class="special">.</span><span class="identifier">size</span><span class="special">()</span> <span class="special">-</span> <span class="number">1</span><span class="special">);</span>
    <span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="number">8</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span> <span class="special">{</span>
        <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">chars</span><span class="special">[</span><span class="identifier">index_dist</span><span class="special">(</span><span class="identifier">rng</span><span class="special">)];</span>
    <span class="special">}</span>
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">cout</span> <span class="special">&lt;&lt;</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">endl</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
      </p>
<div class="calloutlist"><table border="0" summary="Callout list">
<tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_a_random_password.c1"></a><a href="#boost_random.tutorial.generating_a_random_password.c0"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> </p></td>
<td valign="top" align="left"><p>
            We first define the characters that we're going to allow. This is pretty
            much just the characters on a standard keyboard.
          </p></td>
</tr>
<tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_a_random_password.c3"></a><a href="#boost_random.tutorial.generating_a_random_password.c2"><img src="../../../doc/src/images/callouts/2.png" alt="2" border="0"></a> </p></td>
<td valign="top" align="left"><p>
            We use <code class="computeroutput"><a class="link" href="../boost/random/random_device.html" title="Class random_device">random_device</a></code>
            as a source of entropy, since we want passwords that are not predictable.
          </p></td>
</tr>
<tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_a_random_password.c5"></a><a href="#boost_random.tutorial.generating_a_random_password.c4"><img src="../../../doc/src/images/callouts/3.png" alt="3" border="0"></a> </p></td>
<td valign="top" align="left"><p>
            Finally we select 8 random characters from the string and print them
            to cout.
          </p></td>
</tr>
</table></div>
</div>
<div class="section">
<div class="titlepage"><div><div><h3 class="title">
<a name="boost_random.tutorial.generating_quasi_random_line_sphere_intersections"></a><a class="link" href="tutorial.html#boost_random.tutorial.generating_quasi_random_line_sphere_intersections" title="Generating quasi-random line-sphere intersections">Generating
      quasi-random line-sphere intersections</a>
</h3></div></div></div>
<p>
        For the source of this example see <a href="../../..//libs/random/example/intersections.cpp" target="_top">intersections.cpp</a>.
      </p>
<p>
        This example demonstrates generating quasi-randomly distributed chord entry
        and exit points on an S<sup>2</sup> sphere.
      </p>
<p>
        First we include the headers we need for <code class="computeroutput"><a class="link" href="../boost/random/niederreiter_base2.html" title="Type definition niederreiter_base2">niederreiter_base2</a></code>
        and <code class="computeroutput"><a class="link" href="../boost/random/uniform_01.html" title="Class template uniform_01">uniform_01</a></code> distribution.
      </p>
<p>
</p>
<pre class="programlisting"><span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">niederreiter_base2</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">random</span><span class="special">/</span><span class="identifier">uniform_01</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">math</span><span class="special">/</span><span class="identifier">constants</span><span class="special">/</span><span class="identifier">constants</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>

<span class="preprocessor">#include</span> <span class="special">&lt;</span><span class="identifier">boost</span><span class="special">/</span><span class="identifier">tuple</span><span class="special">/</span><span class="identifier">tuple</span><span class="special">.</span><span class="identifier">hpp</span><span class="special">&gt;</span>
</pre>
<p>
      </p>
<p>
        We use 4-dimensional <code class="computeroutput"><a class="link" href="../boost/random/niederreiter_base2.html" title="Type definition niederreiter_base2">niederreiter_base2</a></code>
        as a source of randomness.
      </p>
<p>
</p>
<pre class="programlisting"><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">niederreiter_base2</span> <span class="identifier">gen</span><span class="special">(</span><span class="number">4</span><span class="special">);</span>


<span class="keyword">int</span> <span class="identifier">main</span><span class="special">()</span>
<span class="special">{</span>
  <span class="keyword">typedef</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">tuple</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">,</span> <span class="keyword">double</span><span class="special">,</span> <span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">point_t</span><span class="special">;</span>

  <span class="keyword">const</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">n_points</span> <span class="special">=</span> <span class="number">100</span><span class="special">;</span> <span class="comment">// we will generate 100 points</span>

  <span class="identifier">std</span><span class="special">::</span><span class="identifier">vector</span><span class="special">&lt;</span><span class="identifier">point_t</span><span class="special">&gt;</span> <span class="identifier">points</span><span class="special">;</span>
  <span class="identifier">points</span><span class="special">.</span><span class="identifier">reserve</span><span class="special">(</span><span class="identifier">n_points</span><span class="special">);</span>

  <a class="co" name="boost_random.tutorial.generating_quasi_random_line_sphere_intersections.c0" href="tutorial.html#boost_random.tutorial.generating_quasi_random_line_sphere_intersections.c1"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a><span class="identifier">boost</span><span class="special">::</span><span class="identifier">random</span><span class="special">::</span><span class="identifier">uniform_01</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;</span> <span class="identifier">dist</span><span class="special">;</span>

  <span class="keyword">for</span> <span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">!=</span> <span class="identifier">n_points</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
  <span class="special">{</span>
</pre>
<p>
      </p>
<p>
        Using formula from J. Rovira et al., "Point sampling with uniformly
        distributed lines", 2005 to compute uniformly distributed chord entry
        and exit points on the surface of a sphere.
      </p>
<p>
</p>
<pre class="programlisting"><span class="keyword">double</span> <span class="identifier">cos_theta</span> <span class="special">=</span> <span class="number">1</span> <span class="special">-</span> <span class="number">2</span> <span class="special">*</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">gen</span><span class="special">);</span>
<span class="keyword">double</span> <span class="identifier">sin_theta</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sqrt</span><span class="special">(</span><span class="number">1</span> <span class="special">-</span> <span class="identifier">cos_theta</span> <span class="special">*</span> <span class="identifier">cos_theta</span><span class="special">);</span>
<span class="keyword">double</span> <span class="identifier">phi</span> <span class="special">=</span> <span class="identifier">boost</span><span class="special">::</span><span class="identifier">math</span><span class="special">::</span><span class="identifier">constants</span><span class="special">::</span><span class="identifier">two_pi</span><span class="special">&lt;</span><span class="keyword">double</span><span class="special">&gt;()</span> <span class="special">*</span> <span class="identifier">dist</span><span class="special">(</span><span class="identifier">gen</span><span class="special">);</span>
<span class="keyword">double</span> <span class="identifier">sin_phi</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">sin</span><span class="special">(</span><span class="identifier">phi</span><span class="special">),</span> <span class="identifier">cos_phi</span> <span class="special">=</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">cos</span><span class="special">(</span><span class="identifier">phi</span><span class="special">);</span>

<span class="identifier">point_t</span> <span class="identifier">point_on_sphere</span><span class="special">(</span><span class="identifier">sin_theta</span><span class="special">*</span><span class="identifier">sin_phi</span><span class="special">,</span> <span class="identifier">cos_theta</span><span class="special">,</span> <span class="identifier">sin_theta</span><span class="special">*</span><span class="identifier">cos_phi</span><span class="special">);</span>
</pre>
<p>
      </p>
<p>
        Here we assume that our sphere is a unit sphere at origin. If your sphere
        was different then now would be the time to scale and translate the <code class="computeroutput"><span class="identifier">point_on_sphere</span></code>.
      </p>
<p>
</p>
<pre class="programlisting">  <span class="identifier">points</span><span class="special">.</span><span class="identifier">push_back</span><span class="special">(</span><span class="identifier">point_on_sphere</span><span class="special">);</span>
<span class="special">}</span>
</pre>
<p>
      </p>
<p>
        Vector <code class="computeroutput"><span class="identifier">points</span></code> now holds generated
        3D points on a sphere.
      </p>
<p>
</p>
<pre class="programlisting">  <span class="keyword">return</span> <span class="number">0</span><span class="special">;</span>
<span class="special">}</span>
</pre>
<p>
      </p>
<div class="calloutlist"><table border="0" summary="Callout list"><tr>
<td width="5%" valign="top" align="left"><p><a name="boost_random.tutorial.generating_quasi_random_line_sphere_intersections.c1"></a><a href="#boost_random.tutorial.generating_quasi_random_line_sphere_intersections.c0"><img src="../../../doc/src/images/callouts/1.png" alt="1" border="0"></a> </p></td>
<td valign="top" align="left"><p>
            <code class="computeroutput"><a class="link" href="../boost/random/niederreiter_base2.html" title="Type definition niederreiter_base2">niederreiter_base2</a></code>
            produces integers in the range [0, 2<sup>64</sup>-1]. However, we want numbers in
            the range [0, 1). The distribution <code class="computeroutput"><a class="link" href="../boost/random/uniform_01.html" title="Class template uniform_01">uniform_01</a></code>
            performs this transformation.
          </p></td>
</tr></table></div>
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<td align="right"><div class="copyright-footer">Copyright © 2000-2005 Jens Maurer<br>Copyright © 2009, 2010 Steven Watanabe<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
        file LICENSE_1_0.txt or copy at <a href="http://www.boost.org/LICENSE_1_0.txt" target="_top">http://www.boost.org/LICENSE_1_0.txt</a>)
      </p>
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